One example of conventional high-pressure discharge lamps is a high-pressure mercury-vapor discharge lamp composed of: an arc tube, which is made of quartz glass for example and which has a light-emitting part containing a substantially ellipsoidal inner space; a gas, which is enclosed within the inner space of the light-emitting part and which includes at least mercury and a rare gas; and at least two electrodes, which are arranged in the inner space of the light-emitting part so as to face each other, wherein the lamp satisfies W≧150, P≧250, t≦5, and rl≦0.0103×W−0.00562×P−0.316×rs+0.615×t+1.93, where W (watts) is the power of the lamp during its lighting operation, P (atm) is an operating pressure in the inner space of the light-emitting part, rs (mm) is the shorter radius of the inner space (i.e. the shorter inner radius of the light-emitting part), rl (mm) is the longer radius of the inner space (i.e. the longer inner radius of the light-emitting part) (where rl≧rs), and t (mm) is the wall thickness of the light-emitting part (see Patent Literature 1, for example).
In regard to the high-pressure mercury lamp disclosed in Patent Literature 1, the lamp power W (watts), the operating pressure P (atm), the shorter radius rs (mm) of the inner space of the light-emitting part, the longer radius rl (mm) of the inner space of the light-emitting part, and the wall thickness t (mm) of the light-emitting part satisfy a predetermined relationship when W (watts) is equal to or greater than 200. It is disclosed that when this relationship is satisfied, the stress on the inner surface of the light-emitting part is suppressed to be equal to or less than 5 N/mm2, which prevents breakage of the light-emitting part.